Research

Problem and Background

• Engineering problems frequently require the solution of complex multiphysics equation systems

• A monolithic  strategy is a robust way of handling coupled multiphysics especially in new use cases where coupling strength may be unknown a priori

• A monolithic approach results in a large mixed equation system which is the performance bottleneck for most simulations

Solution Strategy

• Develop block preconditioners which break problems into blocks which are:

  • Solved sequentially in a strategic order

  • Solvable with dedicated single-physics tools (e.g. algebraic multigrid)

  • Smaller than the original problem

• Use physics information to inform block preconditioner design

• Automate preconditioner design process with branch and bound optimization strategy to expand applicability

Early results (in progress)

• Early results show performance saving of 25-80% over state of the art domain decomposition preconditioning depending on problem type and size

Problem and Background

• Traditional ordinary differential equation models for disease spread are effective only for large and well mixed populations

• To detect a dangerous novel pathogen at the early stages of a future pandemic, limited data sets only containing a small number of infections must be used to accurately estimate disease spread parameters

• Agent based models (ABMs) capture stochastic behavior in small populations

• ABMs must be calibrated

Solution

• Use approximate Bayesian computation (ABC) to construct a likelihood function for disease spread parameters given a synthetic data set was observed

• Verified through testing the accuracy of error estimation

Results

• Publication in PLOS One

• Recommendation for calibrating disease spread ABMs

Problem and Background

• Silicon/silicon oxide based field effect transistors (FETS) currently have significant energy losses at high powers and frequencies

• Gallium nitride based FETs offer an alternative for high power high frequency applications

• Unfortunately, current GaNFETs are only made with an expensive deposition based process

• "Printing," or deposition of GaN particles on a chip through fluidic assembly, could dramatically drive down the cost of production

Solution

• Developed method for suspending particles in solution for long enough to print

• Determined method for printing even 200nm layer of GaN particles on silicon

Results

• Successfully created even GaN layers on silicon chips

• Unfortunately, the project eventually lost funding because of trouble forcing the GaN layer to sinter into a coherent layer instead of a collection of particles